This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A238885 #8 Mar 14 2014 00:05:56
%S A238885 1,2,2,1,2,3,2,2,3,2,2,6,1,2,2,6,1,4,2,2,8,2,4,4,2,2,8,2,6,1,8,1,2,2,
%T A238885 10,2,6,2,12,4,2,2,2,10,2,8,2,12,1,12,4,1,2,2,12,2,8,2,16,2,12,6,9,4,
%U A238885 2,2,12,2,10,2,16,2,16,8,1,18,6,4,2,2,14,2
%N A238885 Array: row n gives number of times each possible lower triangular partition L(p) occurs as p ranges through the partitions of n.
%C A238885 Suppose that p is a partition. Let u, v, w be the number of 1's above, on, and below the principal diagonal, respectively, of the Ferrers matrix of p defined at A237981. The lower triangular partition of p, denoted by L(p), is {u,v} if w = 0 and {u,v,w} otherwise.
%C A238885 In row n, the counted partitions are taken in Mathematica order (i.e., reverse lexicographic). A000041 = sum of numbers in row n, and A238886(n) = (number of numbers in row n) = number of lower triangular partitions of n.
%H A238885 Clark Kimberling, <a href="/A238885/b238885.txt">Table of n, a(n) for n = 1..600</a>
%H A238885 Clark Kimberling and Peter J. C. Moses,<a href="http://faculty.evansville.edu/ck6/GalleryThree/Introduction3.html">Ferrers Matrices and Related Partitions of Integers</a>
%e A238885 First 12 rows:
%e A238885 1
%e A238885 2
%e A238885 2 .. 1
%e A238885 2 .. 3
%e A238885 2 .. 2 .. 3
%e A238885 2 .. 2 .. 6 .. 1
%e A238885 2 .. 2 .. 6 .. 1 .. 4
%e A238885 2 .. 2 .. 8 .. 2 .. 4 .. 4
%e A238885 2 .. 2 .. 8 .. 2 .. 6 .. 1 .. 8 .. 1
%e A238885 2 .. 2 .. 10 . 2 .. 6 .. 2 .. 12 . 4 .. 2
%e A238885 2 .. 2 .. 10 . 2 .. 8 .. 2 .. 12 . 1 .. 12 . 4 .. 1
%e A238885 2 .. 2 .. 12 . 2 .. 8 .. 2 .. 16 . 2 .. 12 . 6 .. 9 .. 4
%e A238885 Row 4 arises as follows: there are 3 lower triangular (LT) partitions: 41, 311, 221, of which 41 is produced from the 2 partitions 5 and 11111, while the LT partition 311 is produced by 41 and 2111, and the LT partition 221 is produced by 32, 311, 221; thus row 5 is 2, 2, 3. (For example, the rows of the Ferrers matrix of 311 are (1,1,1), (1,0,0), (1,0,0), with principal diagonal (1,0,0), so that u = 2, v = 1, w = 2; as a partition, 212 is identical to 221.)
%t A238885 ferrersMatrix[list_] := PadRight[Map[Table[1, {#}] &, #], {#, #} &[Max[#, Length[#]]]] &[list]; lt[list_] := Select[Map[Total[Flatten[#]] &, {LowerTriangularize[#, -1], Diagonal[#], UpperTriangularize[#, 1]}] &[ferrersMatrix[list]], # > 0 &]; t[n_] := #[[Reverse[Ordering[PadRight[Map[First[#] &, #]]]]]] &[Tally[Map[Reverse[Sort[#]] &, Map[lt, IntegerPartitions[n]]]]]; u[n_] := Table[t[n][[k]][[1]], {k, 1, Length[t[n]]}]; v[n_] := Table[t[n][[k]][[2]], {k, 1, Length[t[n]]}]; TableForm[Table[t[n], {n, 1, 12}]]
%t A238885 z = 10; Table[Flatten[u[n]], {n, 1, z}]
%t A238885 Flatten[Table[u[n], {n, 1, z}]]
%t A238885 Table[v[n], {n, 1, z}]
%t A238885 Flatten[Table[v[n], {n, 1, z}]] (* A238885 *)
%t A238885 Table[Length[v[n]], {n, 1, z}] (* A238886 *)
%t A238885 (* _Peter J. C. Moses_, Mar 04 2014 *)
%Y A238885 Cf. A238883, A238886, A237981, A000041.
%K A238885 nonn,tabf,easy
%O A238885 1,2
%A A238885 _Clark Kimberling_, Mar 06 2014